This is partly the old story of ego overtaking party commitment. Mrs Petry rapidly became the best known public face of AfD after ousting the party’s founder Bernd Lucke in July 2015, and she might have started to believe she was bigger than the party.

Commentators also need to be more careful in referring to ‘moderate’ and ‘hardline’ factions in AfD. Mrs Petry herself was considered an ‘extremist’ when her faction took over the party two years ago. Most of AfD’s founders had been interested mainly in reforming the EU, and were a very moderate version of UKIP. Mrs Petry and her allies were unafraid of using hardline anti-immigration rhetoric.

This paid off as German voters revolted against conservative Chancellor Angela Merkel’s open door policy on ‘asylum seekers’. At one stage AfD was polling close to 20% and began winning seats in regional parliaments (Landtag) across Germany.

AfD’s candidate for Chancellor, 72-year-old former CDU official Alexander Gauland (right) was unimpressed by Mrs Petry’s behaviour this morning

However Mrs Petry – while happy to use extreme language about immigration and especially about Islam – was very nervous about offending Germany’s small but noisy Jewish population, and wanted to avoid challenging taboo subjects connected to her country’s 20th century history.

Notably she refused to back the leader of anti-Islam group Pegida when he proposed that circumcision of children should be banned until they reach 18 and can decide for themselves. AfD’s draft manifesto in 2016 supported this policy, but Mrs Petry and her allies blocked it, realising that the policy would be seen as anti-Jewish as well as anti-Muslim.

Thuringia Landtag member Bjorn Höcke (centre), one of AfD’s most prominent spokesmen, seen here with Alexander Gauland and Frauke Petry, who later tried to have Höcke expelled from the party

By this time Mrs Petry was engaged in an internal battle within the party to enforce a policy of genuflecting to the national religion of ‘Holocaustianity’. She tried to get one party official, Bjorn Höcke, expelled from AfD – not for ‘Holocaust denial’, but for a speech in which he called the Berlin Holocaust memorial a “monument of shame”, and an interview in which he told the Wall Street Journal: “The big problem is that one presents Hitler as absolutely evil. But of course we know that there is no black and no white in history.”

AfD’s leading candidates at the Bundestag election – Alexander Gauland and Alice Weidel – celebrating their record high vote last night

At this morning’s press conference Mrs Petry did not expand on her reasons for quitting the party. She seems to have the backing of a small faction in the north-eastern state of Mecklenburg-Vorpommern, where four fellow MPs elected yesterday as AfD candidates say they will also now sit as independents.

However the vast majority of the party is likely to view this morning’s outburst as petty and divisive, motivated by personal spite and vanity. Mrs Petry has almost certainly consigned herself to political oblivion. In particular it is difficult for her to sustain the argument that her line is the only “pragmatic” one, after AfD has just secured the best election result it could reasonably have hoped for.

AfD achieved 5.9 million votes (12.6%) and will have 94 seats in the new Bundestag. This is up from 2 million votes (4.7%) at the last general election in 2013, when the party fell just below the 5% threshold so had no seats. AfD’s results were especially outstanding in parts of the former East Germany – becoming the largest party in the region of Saxony (which includes the cities of Leipzig, Dresden and Chemnitz). AfD polled almost 670,000 votes (27.0%) in Saxony, ahead of Merkel’s CDU on 26.9%.

The best NPD constituency result was 2.0% in a Mecklenburg-Vorpommern district close to the Polish border in the far north-east; the party also managed 1.9% in several constituencies in Thuringia and Saxony. NPD polled 1.1% (28,434 votes) in Saxony as a whole, and 1.2% in Thuringia.